Simon Fraser University
Engaging the World

Course Outlines

Fall 2023 - MACM 316 D100

Numerical Analysis I (3)

Class Number: 2181

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 6 – Dec 5, 2023: Mon, Wed, Fri, 12:30–1:20 p.m.
    Burnaby

    Oct 10, 2023: Tue, 12:30–1:20 p.m.
    Burnaby

  • Exam Times + Location:

    Dec 11, 2023
    Mon, 8:30–11:30 a.m.
    Burnaby

  • Prerequisites:

    MATH 152 or 155 or 158, and MATH 232 or 240, and computing experience.

Description

CALENDAR DESCRIPTION:

A presentation of the problems commonly arising in numerical analysis and scientific computing and the basic methods for their solutions. Quantitative.

COURSE DETAILS:


  1. Number systems and errors [1.5 weeks] 
     o Floating point representation, error propagation, error estimation.

  2. Solution of nonlinear equations [2 weeks]
     o Bisection, secant method, Newton's method, fixed-point iteration.

  3. Systems of linear equations [3 weeks]
     o Gaussian elimination (factorization, pivoting, inverse calculation), iterative methods, eigenvalue problems.

  4. Interpolation and approximation [2 weeks]
     o Interpolating polynomials (Lagrange form, error formula), spline interpolation, least-squares fitting.

  5. Differentiation and integration [1.5 weeks]
    o Finite difference approximations of derivatives (error analysis, Richardson extrapolation), quadrature rules for numerical integration.

  6. Initial value problems for ODEs [2 weeks]
     o Euler's method, Taylor and Runge-Kutta methods, convergence, stability.

Grading

  • Quizzes (weekly) 15%
  • Computing Assignments (bi-weekly) 25%
  • I-Clicker Questions 5%
  • Midterm 15%
  • Final Exam 40%

NOTES:

*There will be optional computational office hours scheduled
Mondays from 2:30 PM to 5:30 PM and
Fridays from 2:30 PM to 5:30 PM
in WMC 2820 [math west]. Please plan accordingly.

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks. 
Please pay careful attention to the options discussed in class at the beginning of the semester.

REQUIREMENTS:

Passing grade requires passing exams and computing requirement.

Materials

MATERIALS + SUPPLIES:

I-Clicker questions will be conducted via I-Clicker app. This will require app purchase. Details in class.

REQUIRED READING:

Numerical Analysis
10/E
Burden and Faires
Nelson Canada
ISBN: 9781305253667

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the semester are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.